## Abstract

The Witten index counts the difference in the number of bosonic and fermionic states of a quantum mechanical system. The Schur index, which can be defined for theories with at least N=2 supersymmetry in four dimensions is a particular refinement of the index, dependent on one parameter q serving as the fugacity for a particular set of charges which commute with the hamiltonian and some supersymmetry generators. This index has a known expression for all Lagrangian and some non-Lagrangian theories as a finite dimensional integral or a complicated infinite sum. In the case of N=2 SYM with gauge group U(N) we rewrite this as the partition function of a gas of N non interacting and translationally invariant fermions on a circle. This allows us to perform the integrals and write down explicit expressions for fixed N as well as the exact all orders large N expansion.

Original language | English |
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Article number | 210 |

Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 11 |

DOIs | |

Publication status | Published - 30 Nov 2015 |

## Keywords

- Matrix Models
- Supersymmetric gauge theory